Projections in shapefiles are defined by the Well Known Text that is stored into the .prj file. ESRI is using a bit different dialect and QGIS may not understand that both .prj files mean the same. You can make a test by renaming your .prj from QGIS and using that instead of the one from ESRI. Add also the contents of both .prj files into your question.
– user30184Jun 28 '17 at 12:02

You are right, that made it work properly. Thanks!
– geogrowJun 28 '17 at 13:25